Homogeneity of variance and ANOVA

Assess homogeneity of variance when comparing three independent groups on a continuous outcome

The assumption of homogeneity of variance is the second statistical assumption that needs to be tested for when comparing three or more independent groups on a continuous outcome with ANOVA. Homogeneity of variance is assessed using Levene's Test for Equality of Variances. In order to meet the assumption of homogeneity of variance, the p-value for Levene's Test should above .05. If Levene's Test yields a p-value below .05, then the assumption of homogeneity of variance has been violated.

​Homogeneity of variance essentially makes sure that the distributions of the outcomes in each independent group are comparable and/or equal. If independent groups are not similar in this regard, spurious findings can be yielded. ANOVA should not be conducted on continuous variables that violate the assumption of homogeneity of variance. ANOVA should only be conducted on continuous outcomes between groups that have "equivalent" or similar variances.

The steps for assessing the assumption of homogeneity of variance for ANOVA in SPSS

1. Click Analyze.

2. Drag the cursor over the Compare Means drop-down menu.

3. Click on One-way ANOVA.

4. Click on the continuous outcome variable to highlight it.

5. Click on the arrow to move the outcome variable into the Dependent List: box.

6. Click on the "grouping" variable to highlight it.

7. Click on the arrow to move the "grouping" variable into the Factor: box.

8. Click on the Options button.

9. In the Statistics table, click the Homogeneity of variance test box.

10. Click Continue.

11. Click OK.

The steps for interpreting the SPSS output for homogeneity of variance with ANOVA

In the Test of Homogeneity of Variances table, look under the Sig. column.

If the p-value is MORE THAN .05, then researchers have met the assumption of homogeneity of variance and can conduct a one-way ANOVA.

If the p-value is LESS THAN .05, then researchers have violated the assumption of homogeneity of variance and will use a non-parametric Kruskal-Wallis test to conduct the analysis.

Was the assumption of homogeneity of variance met for ANOVA?

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